I would suspect that it might be more than just commensal bacterial populations on the skin and in the follicles. If the sweat stinks immediately, you may have one or more minor infected follicles. It’s no biggie. It happens all over the body, all the time, but most of our body isn’t ‘designed to capture smell’. It has been hypothesized that pheromone and odor -useful in the animal kingdom- is one function of our vestigial armpit hair, and the substantially different composition of sweat, oil, and other skin glands in our armpits.
Furthermore, the population mix living on various areas of the skin is complex. It’s not a matter of mere innoculation with a contaminated shirt. The various bacteria compete and cooperate, until a balance is reached that is most stable for that region. Staphylococcus aureus, one of the most common and universal skin bacteria, is actually very helpful in that regard. It out-competes other, potentially harmfull bacteria, over the broad expanses of dry exposed skin. In other tissues, it can be less benficial: in the blood, it is (among other things) the primary agent of Toxic shock syndrome; and in the muscle, certain (rare)strains that may already be on your skin might cause Necrotizing Fasciitis (Flesh-eating disease) I wouldn’t worry to much about that last one, though: it’s rare.
If this assymetry of odor really bothers you (or if you simply wish to prove it’s not surface bacteria), simply do this:
Wear an old sweaty T-shirt, backwards, this weekend. If the surface innoculation theory is correct (which I personally doubt), both your armpits will soon stink equally, since both will be heavily innoculated with both bacterial mixtures. With any luck, the less stinky strain will win, but I wouldn’t hold my breath
Or maybe I would. How stinky are they?
True, there are small differences between the temperatures of your two armpit, since they have different circulatory structures (look up brachycephalic trunk and innominate vein, if you really care), but I’d bet on either a temporary infection (if the effect is recent) or a simple assymetry in the distribution of glands (usually unnoticeable)
Barring that, I think highly of the “Preferred hand” innoculation theory. People do use their two hands for varying activities, and therefore the hands, in particular, can be exposed to, and spread different bacteria. There’s a classic tale of why Hindus don’t use their left hand at the table (Oddly, I don’t know if it’s true, though I was raised by Hindus - and I doubt I could get a straight answer from them anyway)